Myeloma cell dynamics in response to treatment supports

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Myeloma cell dynamics in response to treatment supports 1 a model of hierarchical differentiation and clonal evolution 2

Myeloma cell dynamics in response to treatment 3 4

Min Tang1*, Rui Zhao1*, Helgi van de Velde2, Jennifer G. Tross1,3, Constantine 5 Mitsiades4, Suzanne Viselli5, Rachel Neuwirth2, Dixie-Lee Esseltine2, Kenneth 6

Anderson4, Irene M. Ghobrial4, Jesús F. San Miguel6, Paul G. Richardson4, 7 Michael H. Tomasson7, and Franziska Michor1+ 8

9 10 1 Department of Biostatistics and Computational Biology, Dana-Farber Cancer Institute, 11 and Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, 12 MA 02115, USA. 2 Takeda Pharmaceuticals, Inc., Cambridge, MA, 3 Harvard Medical 13 School, Harvard-MIT Division of Health Sciences and Technology, Boston, MA 02115, 14 USA. 4 Dana-Farber Cancer Institute, Boston, USA. 5 Oncology R&D, Janssen Research 15 & Development LLC, Raritan, USA. 6 Hospital Universitario Salamanca, CIC, IBMCC 16 (USAL-CSIC), Salamanca, Spain. 7 Division of Oncology, School of Medicine, 17 Washington University in St. Louis. * Equal contribution. + Author for correspondence. 18 Dana-Farber Cancer Institute, 450 Brookline Avenue, Boston, MA 02215, USA. Tel: 617 19 632 5045. Fax: 617 632 4222. Email: [email protected]. 20 21 22 KEY WORDS: mathematical modeling, multiple myeloma, treatment response 23 24 DISCLOSURE OF CONFLICTS OF INTEREST 25 26 Suzanne Viselli is an employee of Janssen Research and Development. Dixie-Lee 27 Esseltine, Rachel Neuwirth and Helgi van de Velde are employees of Takeda 28 Pharmaceuticals, Inc. Paul Richardson has served on advisory committees for 29 Millennium Pharmaceuticals, Inc., Johnson & Johnson, and Celgene Corporation. 30 31 32 SUPPORT 33 34 We gratefully acknowledge support from the Dana-Farber Cancer Institute Physical 35 Sciences-Oncology Center. 36 37

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TRANSLATIONAL RELEVANCE 38 Relapse in multiple myeloma patients suggests the existence of progenitor cells 39 responsible for tumor regrowth, but this population has never been confirmed. Here, we 40 used mathematical modeling to show that the combined data from three clinical trials of 41 bortezomib-based chemotherapy is consistent with a differentiation hierarchy where a 42 myeloma progenitor cell population that is relatively resistant to therapy gives rise to a 43 differentiated cell population that is sensitive to therapy. Thus, we conclude that 44 bortezomib-based therapy exerts a selection pressure on myeloma cells, and the 45 administration of rational combination treatments may reduce expansion of resistant 46 clones, leading to more prolonged remissions. Our model could be used to improve 47 future clinical trial design for multiple myeloma by using treatment effects of therapeutic 48 agents on both differentiated and progenitor cells populations in order to predict how 49 patients will respond to treatment. 50 51




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ABSTRACT 52 Purpose: Since the pioneering work of Salmon and Durie, quantitative measures of 53 tumor burden in multiple myeloma (MM) have been used to make clinical predictions 54 and model tumor growth. However, such quantitative analyses have not yet been 55 performed on large data sets from trials using modern chemotherapy regimens. 56 Experimental design: We analyzed a large set of tumor response data from three 57 randomized controlled trials of bortezomib-based chemotherapy regimens (total sample 58 size n=1,469 patients) to establish and validate a novel mathematical model of MM cell 59 dynamics. 60 Results: Treatment dynamics in newly diagnosed patients were most consistent with a 61 model postulating two tumor cell subpopulations, “progenitor cells" and “differentiated 62 cells”. Differential treatment responses were observed with significant tumoricidal 63 effects on differentiated cells and less clear effects on progenitor cells. We validated this 64 model using a second trial of newly diagnosed patients and a third trial of refractory 65 patients. When applying our model to data of relapsed patients, we found that a hybrid 66 model incorporating both a differentiation hierarchy and clonal evolution best explains 67 the response patterns. 68 Conclusions: The clinical data, together with mathematical modeling, suggest that 69 bortezomib-based therapy exerts a selection pressure on myeloma cells that can shape 70 the disease phenotype, thereby generating further inter-patient variability. This model 71 may be a useful tool for improving our understanding of disease biology and the 72 response to chemotherapy regimens. 73 74




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INTRODUCTION 75 Multiple myeloma (MM) was the first metastatic malignancy for which quantitative 76 measurements of tumor burden became available, allowing for mathematical and 77 statistical approaches to studying this disease (ref. 1-4). Unlike other cancers for which 78 serial measurements of tumor size are a challenging problem, it was shown in MM that 79 serum levels of myeloma protein (M-protein) is strongly correlated with tumor burden, 80 which allowed for study of the kinetics of this disease (ref. 3). Sullivan and Salmon 81 proposed a mathematical model where tumor growth rate is dependent on the total cell 82 mass (ref. 4), and Hokanson et al. compared this model with a constant growth rate 83 model, using two cell populations with differing drug sensitivities, to describe the 84 dynamics of treatment response in MM patients (ref. 1). Furthermore, Swan and Vincent 85 suggested an optimal dosing strategy based on these models, demonstrating the 86 potential for clinical application of these techniques (ref. 5). However, such quantitative 87 analyses have not yet been performed on large data sets from trials using modern 88 chemotherapy regimens. 89 90 Therapy with melphalan and prednisone has been the standard of care for elderly 91 patients with newly diagnosed multiple myeloma (MM) for more than 40 years (ref. 6, 7). 92 In 2008, the proteasome inhibitor bortezomib (VELCADER) was approved in 93 combination with melphalan and prednisone for treatment of newly diagnosed MM 94 patients not eligible for high-dose chemotherapy, based on the results of the 95 randomized phase III VISTA trial (ref. 8) comparing bortezomib-melphalan-prednisone 96 to melphalan-prednisone treatment. Earlier, bortezomib was approved for treatment of 97




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relapsed multiple myeloma based on the results of the randomized phase III APEX trial 98 (ref. 9, 10) comparing bortezomib monotherapy to dexamethasone treatment. Although 99 in both phase III studies, bortezomib had been able to induce complete tumor 100 responses and significantly prolong survival (ref. 10-12), myeloma relapses eventually 101 occurred and the patients could not be considered cured. Recently the randomized 102 phase II MMY-2001 trial investigating the safety and efficacy of the addition of 103 siltuximab to the bortezomib-melphalan-prednisone regimen showed no survival 104 difference associated with the siltuximab addition (ref. 13). The dynamics of treatment 105 response in these trials have not previously been studied but such efforts would lead to 106 a better understanding of disease mechanisms, which would in turn help inform 107 treatment strategies. Furthermore, the existence of a differentiation hierarchy of MM 108 cells has been suggested (ref. 14), but the effects of chemotherapies on different 109 subpopulations in vivo remain largely unexplored. Here we analyzed the treatment 110 response of MM patients and sought to identify a mechanistic model capable of 111 explaining the trial response data in both newly diagnosed (ref. 11, 13) and relapsed 112 MM patients (ref. 8-10). 113 114 METHODS 115 To develop a model for MM tumor cell dynamics, we utilized data from 682 newly 116 diagnosed MM patients who were treated with first-line melphalan and prednisone with 117 bortezomib (the “VISTA VMP” cohort) or without (the “VISTA MP” cohort) within the 118 randomized phase III VISTA trial (ref. 11) (see SI, “Patient cohorts”). Serum M-protein 119 measurements (g/dl) were analyzed uniformly by a central laboratory and were 120




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determined as surrogates for disease burden (ref. 15). By VISTA trial design, patients 121 were to be treated in both cohorts for a maximum duration of 54 weeks, unless 122 treatment was discontinued earlier due to toxicity or myeloma progression. Of the 682 123 randomized patients, 299 patients in the VISTA MP cohort and 300 patients in the 124 VISTA VMP cohort were evaluated for their disease kinetics (Figure 1a, SI, “Patient 125 selection” for exclusion criteria). To investigate the treatment effects of melphalan, 126 prednisone, and bortezomib, we first utilized a statistical modeling approach to identify 127 trends within the treatment response data (SI, “Statistical modeling”). We then aimed to 128 design simple mathematical models, developed in a biologically intuitive way, to 129 investigate the treatment dynamics of the disease; similar approaches have previously 130 led to a mechanistic understanding of infectious diseases (ref. 16). Finally, we validated 131 our model using M-protein data from two independent trials, the MMY-2001 and APEX 132 trials, which include both newly diagnosed (ref. 11, 13) and relapsed MM patients (ref. 133 8-10). The SI contains details on all patient cohorts, analyses, and models. 134 135 RESULTS 136 We analyzed the observed tumor burden trajectories from the three trials in the 137 following order: 1) we applied statistical modeling to determine the trends in longitudinal 138 tumor trajectories from newly diagnosed MM patients in the VISTA trial, 2) we built two 139 biologically sound mathematical models in an attempt to recapitulate the observed 140 trends, 3) we compared our models’ predictions against observed results, and 4) we 141 validated our model with external data from the independent MMY-2001 and APEX 142 trials and expanded our model to explain trends in refractory patients. 143




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144 Statistical modeling of VISTA trial data 145 Prior to biology-based mathematical modeling, we first investigated different statistical 146 approaches to identify the shape of the treatment response data, i.e. the statistical 147 model with the best fit to the M-protein data (Figure 1d-e, SI, “Statistical modeling”, 148 Figure S1). We began with the data from the VISTA trial, which demonstrated a clear 149 survival advantage for bortezomib, melphalan, and prednisone (VMP) versus melphalan 150 and prednisone alone (MP) in newly diagnosed elderly patients (ref. 11). When studying 151 the cohort-level patient dynamics of treatment response in both the VISTA MP and VMP 152 cohorts, we identified a 2-phasic exponential model (i.e. a curve with a bend, or turning 153 point, Figure S1) to be the best-fitting statistical model among 1-phasic exponential and 154 2-phasic exponential models for both cohorts (SI, “Treatment phase model fitting”, 155 Table 1). The summary statistics for the first slopes ( β1), second slopes ( β2) and turning 156 points (τ ) when fitting 2-phasic exponential models to all patients in each cohort are 157 shown in Table 2. First, we found that patients in the VISTA VMP cohort had a 158 significantly steeper first slope on average than patients in the VISTA MP cohort (p = 159 3x10-15 Wilcoxon rank-sum test), corresponding to a faster initial response rate in the 160 VMP cohort. Second, the difference between the cohorts’ second slopes was not 161 statistically significant (p=0.2439 Wilcoxon rank-sum test), and both cohorts were not 162 significantly different from zero (MP p=0.2645 and VMP p=0.08 t-statistics). Third, the 163 difference between the cohorts’ turning points was also not statistically significant 164 (p=0.3852 Wilcoxon rank-sum test). 165 166




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We then performed individual patient analyses to ensure that the observed patterns at 167 the cohort level are representative of sufficiently many individual patients such that we 168 are not focusing only on a small subset of patients. Comparing between patients who 169 displayed 1- versus 2-phasic exponential declines, we found that there was a 170 significantly larger proportion of 2-phasic patients in the VISTA VMP cohort as 171 compared to the VISTA MP cohort (p ≤ 10-16, Fisher’s exact test). Furthermore, 2-phasic 172 patients in the VISTA VMP cohort had a significantly steeper first slope than such 173 patients in the VISTA MP cohort (p = 3x10-15 for all patients with β1 < 0, Wilcoxon rank-174 sum test), again indicating a faster initial response rate in the VMP cohort. The 175 difference between cohorts in the second slope was not statistically significant. Finally, 176 2-phasic patients in the VISTA VMP cohort had a smaller turning point than patients in 177 the VISTA MP cohort, indicating that the time at which the response rate changes was 178 shorter in the VMP cohort than the MP cohort (p = 0.02 for all 2-phasic patients with β1 < 179 0 and p = 0.01 for all 2-phasic patients with β1 < 0 and β2 < 0, Wilcoxon rank-sum test). 180 181 When investigating the relationship between the best-fitting model and MM stage (ISS 182 stage) (ref. 17), we found that patients with advanced-stage disease in the VISTA MP 183 cohort were significantly more likely to display a 2-phasic rather than a 1-phasic 184 exponential trend after the initiation of therapy (Table S4). For the VISTA VMP cohort, 185 however, there was no significant association between MM stage and the shape of the 186 treatment response curve (Table S4). In both cohorts, there were more deaths of 187 patients with positive second slopes compared to patients with negative second slopes 188 (Table S5). Furthermore, for VISTA VMP patients displaying a 2-phasic M-protein 189




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depletion in the treatment phase, the first slope was significantly associated with the 190 time to progression (p = 0.005, Cox model) when controlling for MM stage. 191 192 Mathematical modeling of VISTA trial data 193 The fact that many patients displayed more complex response kinetics than a simple 194 exponential decay of M-protein abundance over time suggests complex intra-patient 195 disease dynamics. We therefore designed biologically sound mathematical models to 196 explain the response dynamics. These models were created to relate the abundance of 197 measurable M-protein to the numbers of different types of MM cells, which are not 198 directly detectable in the clinical trial data, offering an explanation for the observed trial 199 results from a theoretical biology perspective. To validate the model-predicted and 200 observed outcomes, we compared their turning points and the proportion of 1- and 2-201 phasic patients. 202 203 We first postulated a model based on the existence of two genetically independent MM 204 clones. In this "clonal evolution" model, tumor cells evolve independently and there is no 205 differentiation hierarchy within the myeloma cell population (SI, “The clonal evolution 206 model”). We found that there was a significant difference in the numbers of 1- and 2-207 phasic patients between the observed clinical data in the VISTA trial and the simulated 208 data based on the clonal evolution model (observed 1-phasic patients/total number of 209 patients: 55/249; in one simulation, 1-phasic patients/total number of patients: 113/249; 210 p = 5x10-8, Fisher’s exact test). Furthermore, the estimated turning points for 2-phasic 211 patients were significantly different between the observed clinical data in the VISTA trial 212




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and the simulated data based on the clonal evolution model, 90 ± 69, median 72 days in 213 VISTA data; 186 ± 81, median 169 days in simulated data; p = 2x10-12, two-sample t-214 test (SI, “The clonal evolution model”). Thus, a clonal evolution model, which considers 215 two genetically different MM clones, was unable to recapitulate the tumor dynamics 216 observed from the VISTA trial data. 217 218 We then designed a second model which describes the differentiation hierarchy of the 219 hematopoietic system; in this hierarchical model, we postulated that myeloma cells in 220 part recapitulate normal differentiation and are composed of two populations: myeloma 221 "progenitor” cells and "differentiated” cells (Figure 2a and SI, “The differentiation 222 hierarchy model”). In the context of this model, normal stem cells reside on top of the 223 hierarchy and give rise to progenitor cells, which in turn produce differentiated cells. In 224 addition to normal cells, the bone marrow of MM patients also includes MM cells. MM 225 progenitors reside on top of the MM hierarchy and give rise to MM differentiated cells, 226 which in turn produce M-protein. MM progenitors produce none or only low amounts of 227 M-protein, which we neglected in the mathematical model. We found good agreement 228 between the VISTA trial data and predictions of the mathematical model (Figure 2d-e 229 and SI, “The differentiation hierarchy model”). 230 231 After treatment initiation, the MM cell population declines at the death rate of 232 differentiated MM cells during therapy (equal to the first slope identified in the data, 233 mean -0.0067 for the VISTA MP cohort and -0.0237 for the VISTA VMP cohort) until the 234 latter reach a steady state with MM progenitor cells; from this time onwards, the kinetics 235




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display a shallower decrease signifying the depletion of progenitor cells during 236 treatment (equal to the second slope identified in the data, mean -0.0011 for the VISTA 237 MP cohort and -0.0016 for the VISTA VMP cohort). After treatment discontinuation, 238 some patients show a lasting suppression of their M-protein values, while others 239 experience a disease rebound (Figure S7). In the context of the hierarchical model, 240 these patterns are generated by a selective effect of treatment on different MM clones: 241 treatment may select for MM phenotypes with altered growth and differentiation kinetics 242 as compared to the predominant clone present at the time of diagnosis. In patients in 243 whom no rebound occurs by the end of follow-up, the MM clones that remain after 244 treatment are less “fit” (either via a decreased growth rate or an increased death rate) 245 than those present before treatment. Thus, their expansion occurs on a slower time 246 scale, such that the M-protein value slowly increases after treatment cessation but 247 remains below the detection limit. In patients in whom a rebound occurs, resistant cells 248 slowly outcompete sensitive cells and lead to positive M-protein values after variable 249 periods of time, depending on the size of the resistant clone and their growth rate. 250 251 Validation of the hierarchical model using additional trial data 252 We then utilized data from two independent clinical trials to test the hierarchical model’s 253 ability to explain patient responses: the MMY-2001 trial (ref. 13) comparing bortezomib-254 melphalan-prednisone (VMP) vs. siltuximab plus VMP (SVMP) in newly diagnosed MM 255 patients (n=106, Figure 1b); and the APEX trial comparing high-dose dexamethasone 256 (DEX) vs. single agent bortezomib (VEL) in refractory patients (n=669, Figure 1c). 257 258




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For these two validation data sets, we first performed the same statistical analysis as 259 before to estimate the shapes of the treatment response curves (Figure 1f-i). For both 260 the MMY-2001 and APEX trials, we found that the cohort-level M-protein dynamics 261 during treatment were best explained by the 2-phasic exponential model (Table 1); 262 summary statistics are shown in Table 2. Gratifyingly, we found the first slopes of 263 patients in the VISTA VMP and MMY-2001 VMP cohorts were not significantly different 264 (p=0.2082, t test). For the MMY-2001 trial, we found that there was a statistically 265 significant difference between VMP and SVMP cohorts in terms of the first slopes 266 (p=0.0005, t test). Interestingly, although the addition of siltuximab significantly 267 increased the initial reduction of M-protein levels, it failed to improve progression-free of 268 overall survival (ref. 13). In terms of the second slopes, there was no significant 269 difference between MMY-2001 VMP and SVMP cohorts (p=0.7586, t test), and both 270 cohorts were not significantly different from zero (VMP p= 0.8953 and SVMP p=0.2123, 271 t test). For the APEX trial, we found that patients in the VEL cohort had a significantly 272 steeper first slope than patients in the DEX cohort (p = 0.0035 t test). Also, the 273 difference between cohorts in terms of the second slope was not statistically significant 274 (p=0.8635 t test). However, unlike the VISTA and MMY-2001 trials, in the APEX trial the 275 second slopes were significantly positive (DEX p=0.01231 and VMP p=0.001 t-276 statistics). These increases are consistent with disease progression and likely signify 277 the development of drug-resistant MM cells. In all three trials, patients displayed 278 significant reductions in M-protein levels immediately upon receiving bortezomib-based 279 treatment; however, the long-term effects of these medications varied. 280 281




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We then aimed to validate the hierarchical model using data from the MMY-2001 and 282 the APEX trials. We found that, for the MMY-2001 trial consisting of newly diagnosed 283 patients, the hierarchical model was able to recapitulate the population-level M-protein 284 trajectories; the MMY-2001 VMP cohort could be recapitulated using the same 285 parameters as for the VISTA VMP cohort (Figure 2g). The correlations between 286 observed mean, median and model predicted values were 0.82 and 0.78, respectively. 287 The SVMP cohort could be recapitulated using slope estimates obtained from the 288 SVMP patient data and keeping all other parameters unchanged (Figure 2f and Table 289 2). 290 291 For the APEX trial, we observed increasing trends in M-protein values already during 292 the treatment phase in many patients; this was not unexpected as the time to myeloma 293 progression is shorter in relapsed MM than in newly diagnosed MM, and therefore for 294 many patients in the APEX trial, this time fell within the trial-specified treatment duration. 295 First, among patients displaying 1-phasic patterns, more patients in the APEX trial had 296 statistically significant positive slopes ( β1>0 and p<0.05; APEX DEX: 4/94 and APEX 297 VEL: 11/83) than in the VISTA trial (VISTA MP: 3/153 and VISTA VMP: 0/55). Second, 298 for patients displaying 2-phasic patterns in the APEX trial, we observed rebounds 299 ( β2>0) in the M-protein values during treatment (Table 2 and Figure S9). Initially, 2-300 phasic patients in both trials had similar responses to treatment, as shown by the 301 decline in M-protein values immediately after treatment initiation and the similarity in the 302 magnitudes of β1 . However, the long-term treatment response differed between the 303 APEX and VISTA patients. We observed that, among patients who displayed 2-phasic 304




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trends, relapsed patients in the APEX trial were more likely to have statistically 305 significant rebounds ( β2>0 and p<0.05; APEX DEX: 22/49 and APEX VEL: 31/85) than 306 the newly diagnosed patients in the VISTA trial (VISTA MP: 19/102 and VISTA VMP: 307 27/194). In addition, most rebounding patients in the APEX trial had M-protein rebounds 308 within 100 days after the start of treatment, while still on treatment (median: 74.21 days; 309 mean: 83.20; sd: 41.88 for the rebounding patients in the APEX DEX cohort and 310 median: 68.02 days; mean: 69.14; sd: 27.80 for the rebounding patients in the APEX 311 VEL cohort). 312 313 Development of a hybrid mathematical model for MM cell dynamics 314 Based on these observations, we attributed the differences in M-protein dynamics 315 between newly diagnosed and relapsed patients to the existence and expansion of a 316 resistant clone in relapsed patients (Figure 3a). A dominant resistant clone existing 317 prior to treatment explains the increasing M-protein values during treatment among 1-318 phasic patients in the APEX trial; an expanding resistant clone during treatment 319 explains the initial declines followed by increases in M-protein values; and the presence 320 of a small resistant clone explains continuing 2-phasic declines in the remaining patients 321 (Figure 3b-d). Therefore, we extended our mathematical model to take into account 322 resistant clone(s) (Figure 3a, SI, “The hybrid model”). In this extended model, in 323 addition to normal cells and sensitive MM cells, there is a resistant clone that originally 324 arose from the sensitive progenitor MM cells. This resistant clone gives rise to a similar 325 differentiation hierarchy as the sensitive cells. The observed M-protein values are the 326 sum of M-protein values generated from the sensitive and resistant clones; the amount 327




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of M-protein secreted by each clone is proportional to the size of the clone and the 328 relative secretion rates, which are considered to be similar. The time at which resistance 329 arises determines the relative proportion of sensitive and resistant cells. In newly 330 diagnosed patients, the M-protein contribution from the resistant cells during treatment 331 is negligible; this is supported by the observation that only a relatively small number of 332 patients (7 and 21% in VISTA VMP and MP cohorts, respectively) experienced 333 increases in M-protein values while on treatment in the VISTA trial. In contrast, in the 334 relapsed patients from the APEX trial, due to prior treatment-induced clonal selection, 335 the M-protein contribution from the resistant clone is sufficiently large and stable in size 336 (between 1% and 10%) to alter the treatment response trajectory, leading to rebounds 337 in a subset of patients while on treatment in the APEX trial (SI, “Rebound dynamics”). 338 Unlike the clonal expansion model, the resistant cells do not need to be substantial in 339 size at the beginning of the first treatment to drive the rebound trajectory; rather, 340 through multiple rounds of treatment-induced selection, the fraction of resistant cells 341 may increase sufficiently much to alter the response trajectory. This hybrid model was 342 able to explain the M-protein dynamics for both newly diagnosed and relapsed myeloma 343 patients in response to chemotherapy (Figure 2d-e and Figure 3e-f). Our model 344 suggests that treatment-induced clonal selection may contribute to the increases of the 345 M-protein levels in the refractory patients while on treatment. 346 347 DISCUSSION 348 Here, we present a comprehensive quantitative analysis of myeloma cell growth and 349 treatment response based on three large randomized trials (total sample size n=1,469). 350




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Our analysis of responses to induction therapy in newly diagnosed patients in the 351 VISTA trial revealed complex but structured kinetic patterns that support a hierarchical 352 two-cell population mathematical model for MM. This model was able to recapitulate the 353 observed two-phasic decline patterns observed in the majority of newly diagnosed 354 patients. Importantly, an alternative clonal selection model of myeloma cell growth did 355 not fit the trial data. The hierarchical model suggests the existence of a MM progenitor 356 cell population that has self-renewal capacity and distinct growth kinetics and gives rise 357 to the differentiated MM cell population. The observation of a significantly larger 358 proportion of 2-phasic patients in the VISTA VMP cohort as compared to the VISTA MP 359 cohort when performing the individual level analysis signifies the potential treatment 360 effect of bortezomib in combination with melphalan and prednisone on increasing the 361 death rate of MM progenitor cells during therapy. Our model of MM progenitors, which 362 are non-secretory and relatively drug-resistant compared to differentiated cells, is 363 supported by experimental evidence (ref. 18-20). 364 365 We used the two additional independent sets of clinical trial data to validate and extend 366 the hierarchical model. All trial data supported the model for disease response to 367 treatment; however, inter-patient variability of disease kinetics was noted to be 368 significant at the time of disease relapse, requiring the adjustment of growth parameters 369 in the model and suggesting that distinct MM progenitor subclones were selected by 370 induction treatment. The existence of clonal selection between myeloma subclones was 371 also supported by the analysis of relapsed or refractory patients in the APEX trial. The 372 varied trajectories of disease relapse observed necessitated the development of a 373




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hybrid model with preexisting drug-resistant myeloma cell clones. Importantly, 374 mathematical modeling in myeloma has not been attempted previously on this scale. In 375 addition, statistical analyses reveal different M-protein trajectories even among patients 376 randomly assigned to the same treatment cohorts. Significant association between 377 slopes in M-protein trajectories and survival outcomes have been observed. Hence, M-378 protein trajectories may have the potential to serve as a key second endpoint for the 379 early detection of disease relapse. 380 381 Our approach evaluated myeloma cell behavior unbiased by prior assumptions, by 382 analyzing available patient data without a priori defined patient subgroups. If 383 quantitative data on the effect of patient-specific mutations on cell growth, for example, 384 become available, the model might be further refined. Recent studies (ref. 21-23) 385 documented pronounced intra-patient genetic heterogeneity in human neoplasias and 386 attributed disease progression and drug resistance to the differential molecular features 387 of the underlying tumor subclones. However, it remains a formal possibility that the 388 functional heterogeneity within a tumor as described by our model will not be genetically 389 determined but rather controlled by microenvironmental or epigenetic factors. 390 Elucidating the pathways that control functional heterogeneity among subclones is 391 experimentally challenging, but mathematical modeling can address these limitations 392 and provide insights into the effects of novel treatments on tumor cell dynamics and 393 how they determine the behavior of human cancers. 394 395




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A strength of our model is that it is based on in vivo patient data. Our model is agnostic 396 in regards to the identity of progenitor and differentiated myeloma cells and 397 mechanisms of disease resistance. Our analysis is consistent with reports of clonogenic 398 B-cell "MM stem cells" isolated from patient samples (ref. 14, 24). However, 399 experimental data are divided on whether MM progenitor cells are in fact contained 400 within the CD138- cell compartment (ref. 25-27). Additional surface markers may be 401 needed to identify MM progenitor cells, but alternative biological explanations are also 402 possible. MM progenitors may be a functionally distinct subset of MM cells defined by 403 something other than markers of normal B-cell maturation, e.g. by stromal cell 404 interactions (ref. 28, 29). Alternatively, two-phase response kinetics might be explained 405 by yet undefined drug metabolism induced over time (although published 406 pharmacokinetic data on bortezomib are not consistent with this hypothesis) (ref. 30), or 407 by the induction of immune or other host responses activated after treatment initiation. 408 Mechanisms of disease resistance have been identified in MM, and additional 409 experiments will be required to determine which mechanisms explain in vivo resistance 410 observed in clinical trials. However, our model was examined in clinical trials with a 411 bortezomib-based therapy. The kinetics of tumor growth may be different with 412 immunomodulatory agents such as lenalidomide or pomalidomide when used alone or 413 in combination with proteasome inhibitors. Future studies to examine these kinetics 414 would be interesting to determine whether these agents have similar effects on 415 progenitor cell populations and heterogeneous clonal populations. Another caveat of our 416 study is that measurement of tumor burden in MM is based on M-protein level in the 417




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peripheral blood. Our model may not be predictive if the therapeutic agent inhibits 418 secretion of M-protein or induces a cytostatic and not cytotoxic effect on the tumor cells. 419 420 The current goal of treatment in MM is to achieve deep complete remissions. 421 Mathematical modeling based on treatment responses can provide an additional 422 method for testing biological hypotheses relevant to disease outcomes in patients with 423 MM. Here, we presented a model based on a large amount of available clinical data, but 424 models such as this one can also be used to improve the design of new clinical trials in 425 myeloma by using treatment effects of specific agents on both differentiated and 426 progenitor cells populations as endpoints (ref. 31). Mathematical modeling as suggested 427 here might eventually be useful for investigating the efficacies of novel treatment 428 modalities. For instance, if the effects of an agent on individual myeloma cell 429 populations are known, our mathematical model can help predict how diverse patient 430 populations will respond to treatment. As multiple MM clones are present at diagnosis, 431 the administration of rational combination treatments at relapse may reduce their 432 expansion and therefore lead to deeper and more prolonged remissions, again an area 433 where the model may have utility (ref. 32, 33). Finally, mathematical models are limited 434 by the availability of uniformly collected quantitative patient data. The utility of 435 mathematical models such as this one would be improved by collecting additional 436 quantitative data centrally from future clinical trials. 437 438 MATERIALS AND METHODS 439 Supplementary Information is available on Clinical Cancer Research’s website. 440




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441 AUTHOR CONTRIBUTIONS 442 M.T., R.Z., H.V.D.V., M.T., and F.M. designed the study. M.T., R.Z. and F.M. performed 443 the analyses and investigated the results. All authors contributed data and/or analysis 444 tools and wrote the paper. 445 446 ACKNOWLEDGEMENTS 447 We would like to thank the Michor lab, Mithat Gonen, Katherine Weilbaecher, Rameen 448 Beroukhim, Victor DeGruttola, and Paul Catalano for helpful discussions, and also 449 especially thank all the participating patients, their families, the research teams and the 450 clinical investigators in the VISTA, MMY-2001 and APEX studies. We gratefully 451 acknowledge support from the Dana-Farber Cancer Institute Physical Sciences-452 Oncology Center. 453 454 DISCLOSURE OF CONFLICTS OF INTEREST 455 Suzanne Viselli is an employee of Janssen Research and Development. Dixie-Lee 456 Esseltine, Rachel Neuwirth, and Helgi van de Velde are employees of Takeda 457 Pharmaceuticals, Inc. Paul Richardson has served on advisory committees for 458 Millennium Pharmaceuticals, Inc., Johnson & Johnson, and Celgene Corporation. 459 460 REFERENCES 461 1. Hokanson JA, Brown BW, Thompson JR, Drewinko B, Alexanian R. Tumor growth 462 patterns in multiple myeloma. Cancer 1977; 39(3): 1077-1084. 463 464




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FIGURE LEGENDS 588 589 Figure 1. Patient selection criteria and M-protein treatment response in the VISTA 590 and APEX trials. (a-c) Flowcharts outlining the patient inclusion and exclusion criteria 591 for quantitative analysis of M-protein treatment response. (d-i) Median longitudinal M-592 protein trajectories for each cohort in the three trials, and the associated numbers of 593 patients at each time point: d): VISTA MP cohort, e): VISTA VMP cohort, f): MMY2001 594 VMP cohort, g): MMY2001 SVMP cohort, h): APEX DEX cohort and i): APEX VEL 595 cohort. The median M-protein values are indicated by the orange circles, and quartiles 596 are indicated by the whiskers. The numbers of patients at each time point are shown by 597 the histograms. Vertical yellow and green dashed lines indicate treatment initiation and 598 termination times, respectively. For the VISTA and MMY-2001 trials (panels d-g), only 599 patients who completed the entire treatment regimen are included. For the APEX trial 600 (panel h-i), due to the small number of patients who completed the entire treatment 601 regimen, only the M-protein response during treatment is shown. 602 603 Figure 2. The hierarchical mathematical model accurately predicts the dynamics 604 of M-protein response in the VISTA and MMY-2001 trials. (a) Illustration of the 605 hierarchical mathematical model. Normal and MM cells are shown in black and blue, 606 respectively. Solid downward arrows indicate the direction in the differentiation 607 hierarchy. Circular arrows indicate cellular regeneration within each differentiation level. 608 Double-lined arrow indicates M-protein production from differentiated MM cells. (b-c) 609 The panels display the model-predicted abundances of normal (black) stem cells, 610




25

normal (black) and MM (blue) progenitor cells, and normal (black) and MM (blue) 611 differentiated cells over time (years) for the VISTA MP (panel b) and VISTA VMP (panel 612 c) cohorts since the emergence of the first MM cell, as predicted by the mathematical 613 framework (see SI, “The differentiation hierarchy model”). The pink shaded region 614 denotes the time during which patients receive treatment. (d-g) Concordance between 615 observed population-level MM protein trajectories (blue intervals, error bars indicating 616 the observed quartiles) and the MM protein levels predicted by the mathematical model 617 (solid blue lines). The parameter values for the first and second slopes used to generate 618 panels d, e, and f are listed in Table 2. For panel g, the model predicted trajectory is 619 generated using the same first and second slopes as panel e. All ancillary parameters 620 for panels d-g are identical and are listed in SI, “Parameter values for the hierarchical 621 and hybrid models.” 622 623 Figure 3. The hybrid mathematical model accurately predicts the dynamics of M-624 protein response in all three trials. (a) Illustration of the hybrid mathematical model. 625 Normal, sensitive, and resistant MM cells are shown in black, blue, and red, 626 respectively. The dashed arrow indicates the mutation event that gives rise to the first 627 resistant cell. Solid downward arrows indicate the direction in the differentiation 628 hierarchy. Circular arrows indicate cell regeneration within each differentiation level. 629 Double-lined arrow indicates the production of M-protein from differentiated MM cells. 630 (b) Illustration of effects of the time at which resistance arises on the observed M-631 protein trajectories. Left: resistance emerges very early; middle: resistance emerges 632 early; right: resistance emerges late. The blue lines denote the contribution to the 633




26

changes in the observed M-protein values of sensitive MM cells; the red lines denote 634 the contribution to the changes in the observed M-protein values of resistant MM cells; 635 and the black dots represent the observed total M-protein levels from both sensitive and 636 resistant MM cells. Although the sensitive cells’ response to treatment remains identical 637 in all three subpanels, the timing at which resistance arises determines the observed M-638 protein response. Similar to the VISTA trial, the initial steep decline in M-protein (middle 639 and right subpanels) is attributed to the reduction in the sensitive differentiated MM 640 cells; the shallow decline in M-protein is interpreted as the result of the reduction in the 641 number of sensitive MM progenitor cells. Vertical dashed lines in yellow and green 642 indicate treatment start and end dates. (c-d) The panels display the model-predicted 643 abundances of normal (black) stem cells; normal (black), sensitive MM (blue), and 644 resistant MM (red) progenitor cells; and normal (black), sensitive MM (blue), and 645 resistant MM (red) differentiated cells over time (years) for early (c) vs. late (d) 646 emergence of resistance for the APEX DEX cohort, as predicted by the mathematical 647 framework (see SI, “The hybrid model”). Panels (c) and (d) have identical parameter 648 values except for the time at which resistance arises (for the full set of parameter 649 values, see SI, “Parameter values for the hierarchical and hybrid models”). The time at 650 which resistance arises dictates whether a rebound occurs during the treatment phase. 651 (e-f) M-protein treatment response dichotomized based on rebound status for APEX 652 DEX and VEL cohorts. Rebound during treatment (purple): patients with at least one 653 positive slope during the treatment phase; no rebound during treatment (orange): 654 patients with all negative slope(s) during the treatment phase. Observed median M-655 protein values (≥10 observations) from each subgroup are shown in dots. Lines show 656




27

model-predicted M-protein trajectories. Within each cohort, all parameter values are 657 identical, except the time at which resistance arises (for the full set of parameter values, 658 see SI, “Parameter values for the hierarchical and hybrid models,” and Supplementary 659 Table S7). 660




1

Table 1. Summary statistics of the treatment response data analysis. The table displays statistics on the individual patient model fitting as well as whole cohort model fitting for the cohorts for the three trials during treatment. See SI, “Treatment phase model fitting”, for details.

VISTA MP cohort during treatment

(255 patients)

VISTA VMP cohort during

treatment (249 patients)

2-phasic exponential model

Exponential model


Exponential model

Min* of Ri2 0.089 0 0.174 0.002

1st Quartile* of Ri2 0.678 0.327 0.874 0.374

Median* of Ri2 0.865 0.629 0.929 0.645

Mean* of Ri2 0.787 0.572 0.889 0.577

3rd Quartile* of Ri2 0.938 0.847 0.962 0.813

Max* of Ri2 0.999 0.980 1 0.955

**Final 0.902 0.706 0.910 0.642 ***Sum of BICs -1096.8 -978.9 -773.1 -480.5

MMY-2001 VMP cohort during treatment

(40 patients)

MMY-2001 SVMP cohort

during treatment (38 patients)


Exponential model


Exponential model

Min* of Ri2 0.684 0.007 0.187 0.003

1st Quartile* of Ri2 0.872 0.444 0.876 0.250

Median* of Ri2 0.926 0.630 0.948 0.399

Mean* of Ri2 0.912 0.573 0.883 0.473

3rd Quartile* of Ri2 0.968 0.731 0.968 0.773

Max* of Ri2 0.999 0.938 1 0.950

**Final 0.929 0.640 0.934 0.471 ***Sum of BICs -313.9 -241.5 -309.5 -214.8

APEX DEX cohort during treatment

(143 patients)

APEX VEL cohort during

treatment (168 patients)

2-phasic exponential

Exponential model

2-phasic exponential

Exponential model




2

model model Min* of Ri

2 0.054 0.000 0.228 0.0001st Quartile* of Ri

2 0.716 0.105 0.828 0.195Median* of Ri

2 0.846 0.370 0.937 0.529Mean* of Ri

2 0.799 0.404 0.873 0.4983rd Quartile* of Ri

2 0.944 0.684 0.983 0.777Max* of Ri

2 1.000 0.964 1.000 0.996**Final 0.830 0.496 0.898 0.580***Sum of BICs -1402.5 -1201.4 -1729.7 -1376.1

* the Minimum/1st Quartile/Median/Mean/3rd Quartile/Maximum of the Ri

2, i = 1, …, N, calculated from the corresponding fitted model for each individual patient, where N is the total number of patients and Ri

2 = 1 - SSEi / SSTi; ** Final , calculated as 1 - SSEi / SSTi, evaluates the overall fit of the corresponding model to the whole time series data with all patients for each cohort; *** Sum of BICs is the sum of BICs over all subjects for each cohort.




1

Table 2. Summary statistics of slopes and turning points in the treatment response data. The table displays the means of the first ( β1) and second ( β2) slopes as well as the turning points (τ ) obtained from fitting a bi-phasic model to each cohort. Cohort (# patients)

First slope, β1 (standard deviation)

Second slope, β2 (standard deviation)

Turning point, τ (standard deviation)

VISTA MP (255) -0.0067 (0.0094) -0.0011 (0.0162) 116.20 (87.02) VISTA VMP (249) -0.0237 (0.0217) -0.0016 (0.0145) 106.20 (77.59)

MMY-2001 VMP (40) -0.0192(0.0153) 0.0004(0.0191) 151.55(80.05)

MMY-2001 SVMP (38) -0.0530(0.0562) 0.0014(0.0068) 106.61(75.89)

APEX DEX (143) -0.0169 (0.0151) 0.0037 (0.0175) 67.1 (44.75) APEX VEL (168) -0.0285 (0.0243) 0.0034 (0.0132) 70.1 (40.06)













Published OnlineFirst March 22, 2016.Clin Cancer Res Min Tang, Rui Zhao, Helgi van de Velde, et al. model of hierarchical differentiation and clonal evolutionMyeloma cell dynamics in response to treatment supports a

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